Enhanced push-pull (epp) waveforms for achieving primary color sets in multi-color electrophoretic displays

ABSTRACT

Enhanced push pull driving waveforms for driving a four particle electrophoretic medium including four different types of particles, for example a set of scattering particles and three sets of subtractive particles. Methods for identifying a preferred waveform for a target color state when using a voltage driver having at least five different voltage levels.

RELATED APPLICATIONS

This application is a continuation of U.S. patent application Ser. No.17/515,838 filed on Nov. 1, 2021, which claims priority to U.S.Provisional Patent Application No. 63/108,521, filed Nov. 2, 2020, bothof which applications are incorporated by reference in their entireties.All patents and publications disclosed herein are also incorporated byreference in their entireties.

BACKGROUND

An electrophoretic display (EPD) changes color by modifying the positionof a charged colored particle with respect to a light-transmissiveviewing surface. Such electrophoretic displays are typically referred toas “electronic paper” or “ePaper” because the resulting display has highcontrast and is sunlight-readable, much like ink on paper.Electrophoretic displays have enjoyed widespread adoption in eReaders,such as the AMAZON KINDLE® because the electrophoretic displays providea book-like reading experience, use little power, and allow a user tocarry a library of hundreds of books in a lightweight handheld device.

For many years, electrophoretic displays included only two types ofcharged color particles, black and white. (To be sure, “color” as usedherein includes black and white.) The white particles are often of thelight scattering type, and comprise, e.g., titanium dioxide, while theblack particle are absorptive across the visible spectrum, and maycomprise carbon black, or an absorptive metal oxide, such as copperchromite. In the simplest sense, a black and white electrophoreticdisplay only requires a light-transmissive electrode at the viewingsurface, a back electrode, and an electrophoretic medium includingoppositely charged white and black particles. When a voltage of onepolarity is provided, the white particles move to the viewing surface,and when a voltage of the opposite polarity is provided the blackparticles move to the viewing surface. If the back electrode includescontrollable regions (pixels)— either segmented electrodes or an activematrix of pixel electrodes controlled by transistors— a pattern can bemade to appear electronically at the viewing surface. The pattern canbe, for example, the text to a book.

More recently, a variety of color option have become commerciallyavailable for electrophoretic displays, including three-color displays(black, white, red; black white, yellow), and four color displays(black, white, red, yellow). Similar to the operation of black and whiteelectrophoretic displays, electrophoretic displays with three or fourreflective pigments operate similar to the simple black and whitedisplays because the desired color particle is driven to the viewingsurface. The driving schemes are far more complicated than only blackand white, but in the end, the optical function of the particles is thesame.

Advanced Color electronic Paper (ACeP™) also includes four particles,but the cyan, yellow, and magenta particles are subtractive rather thanreflective, thereby allowing thousands of colors to be produced at eachpixel. The color process is functionally equivalent to the printingmethods that have long been used in offset printing and ink-jetprinters. A given color is produced by using the correct ratio of cyan,yellow, and magenta on a bright white paper background. In the instanceof ACeP, the relative positions of the cyan, yellow, magenta and whiteparticles with respect to the viewing surface will determine the colorat each pixel. While this type of electrophoretic display allows forthousands of colors at each pixel, it is critical to carefully controlthe position of each of the (50 to 500 nanometer-sized) pigments withina working space of about 10 to 20 micrometers in thickness. Obviously,variations in the position of the pigments will result in incorrectcolors being displayed at a given pixel. Accordingly, exquisite voltagecontrol is required for such a system. More details of this system areavailable in the following U.S. Patents, all of which are incorporatedby reference in their entireties: U.S. Pat. Nos. 9,361,836, 9,921,451,10,276,109, 10,353,266, 10,467,984, and 10,593,272.

This invention relates to waveforms for driving color electrophoreticdisplays, especially, but not exclusively, electrophoretic displayscapable of rendering more than two colors using a single layer ofelectrophoretic material comprising a plurality of colored particles,for example white, cyan, yellow, and magenta particles. In someinstances two of the particles will be positively-charged, and twoparticles will be negatively-charged. In some instances, onepositively-charged particle will have a thick polymer shell and onenegatively-charged particle has a thick polymer shell.

The term gray state is used herein in its conventional meaning in theimaging art to refer to a state intermediate two extreme optical statesof a pixel, and does not necessarily imply a black-white transitionbetween these two extreme states. For example, several of the E Inkpatents and published applications referred to below describeelectrophoretic displays in which the extreme states are white and deepblue, so that an intermediate gray state would actually be pale blue.Indeed, as already mentioned, the change in optical state may not be acolor change at all. The terms black and white may be used hereinafterto refer to the two extreme optical states of a display, and should beunderstood as normally including extreme optical states which are notstrictly black and white, for example the aforementioned white and darkblue states.

The terms bistable and bistability are used herein in their conventionalmeaning in the art to refer to displays comprising display elementshaving first and second display states differing in at least one opticalproperty, and such that after any given element has been driven, bymeans of an addressing pulse of finite duration, to assume either itsfirst or second display state, after the addressing pulse hasterminated, that state will persist for at least several times, forexample at least four times, the minimum duration of the addressingpulse required to change the state of the display element. It is shownin U.S. Pat. No. 7,170,670 that some particle-based electrophoreticdisplays capable of gray scale are stable not only in their extremeblack and white states but also in their intermediate gray states, andthe same is true of some other types of electro-optic displays. Thistype of display is properly called multi-stable rather than bistable,although for convenience the term bistable may be used herein to coverboth bistable and multi-stable displays.

The term impulse, when used to refer to driving an electrophoreticdisplay, is used herein to refer to the integral of the applied voltagewith respect to time during the period in which the display is driven.The term waveform, when used to refer to driving an electrophoreticdisplay is used to describe a series or pattern of voltages provided toan electrophoretic medium over a given time period (seconds, frames,etc.) to produce a desired optical effect in the electrophoretic medium.

A particle that absorbs, scatters, or reflects light, either in a broadband or at selected wavelengths, is referred to herein as a colored orpigment particle. Various materials other than pigments (in the strictsense of that term as meaning insoluble colored materials) that absorbor reflect light, such as dyes or photonic crystals, etc., may also beused in the electrophoretic media and displays of the present invention.

Particle-based electrophoretic displays have been the subject of intenseresearch and development for a number of years. In such displays, aplurality of charged particles (sometimes referred to as pigmentparticles) move through a fluid under the influence of an electricfield. Electrophoretic displays can have attributes of good brightnessand contrast, wide viewing angles, state bistability, and low powerconsumption when compared with liquid crystal displays. Nevertheless,problems with the long-term image quality of these displays haveprevented their widespread usage. For example, particles that make upelectrophoretic displays tend to settle, resulting in inadequateservice-life for these displays.

As noted above, electrophoretic media require the presence of a fluid.In most prior art electrophoretic media, this fluid is a liquid, butelectrophoretic media can be produced using gaseous fluids; see, forexample, Kitamura, T., et al., Electrical toner movement for electronicpaper-like display, IDW Japan, 2001, Paper HCS1-1, and Yamaguchi, Y., etal., Toner display using insulative particles charged triboelectrically,IDW Japan, 2001, Paper AMD4-4). See also U.S. Pat. Nos. 7,321,459 and7,236,291. Such gas-based electrophoretic media appear to be susceptibleto the same types of problems due to particle settling as liquid-basedelectrophoretic media, when the media are used in an orientation whichpermits such settling, for example in a sign where the medium isdisposed in a vertical plane. Indeed, particle settling appears to be amore serious problem in gas-based electrophoretic media than inliquid-based ones, since the lower viscosity of gaseous suspendingfluids as compared with liquid ones allows more rapid settling of theelectrophoretic particles.

Numerous patents and applications assigned to or in the names of theMassachusetts Institute of Technology (MIT) and E Ink Corporationdescribe various technologies used in encapsulated electrophoretic andother electro-optic media. Such encapsulated media comprise numeroussmall capsules, each of which itself comprises an internal phasecontaining electrophoretically-mobile particles in a fluid medium, and acapsule wall surrounding the internal phase. Typically, the capsules arethemselves held within a polymeric binder to form a coherent layerpositioned between two electrodes. The technologies described in thesepatents and applications include:

-   -   (a) Electrophoretic particles, fluids and fluid additives; see        for example U.S. Pat. Nos. 7,002,728 and 7,679,814;    -   (b) Capsules, binders and encapsulation processes; see for        example U.S. Pat. Nos. 6,922,276 and 7,411,719;    -   (c) Microcell structures, wall materials, and methods of forming        microcells; see for example U.S. Pat. Nos. 7,072,095 and        9,279,906;    -   (d) Methods for filling and sealing microcells; see for example        U.S. Pat. Nos. 7,144,942 and 7,715,088;    -   (e) Films and sub-assemblies containing electro-optic materials;        see for example U.S. Pat. Nos. 6,982,178 and 7,839,564;    -   (f) Backplanes, adhesive layers and other auxiliary layers and        methods used in displays; see for example U.S. Pat. Nos.        7,116,318 and 7,535,624;    -   (g) Color formation color adjustment; see for example U.S. Pat.        Nos. 6,017,584; 6,545,797; 6,664,944; 6,788,452; 6,864,875;        6,914,714; 6,972,893; 7,038,656; 7,038,670; 7,046,228;        7,052,571; 7,075,502; 7,167,155; 7,385,751; 7,492,505;        7,667,684; 7,684,108; 7,791,789; 7,800,813; 7,821,702;        7,839,564; 7,910,175; 7,952,790; 7,956,841; 7,982,941;        8,040,594; 8,054,526; 8,098,418; 8,159,636; 8,213,076;        8,363,299; 8,422,116; 8,441,714; 8,441,716; 8,466,852;        8,503,063; 8,576,470; 8,576,475; 8,593,721; 8,605,354;        8,649,084; 8,670,174; 8,704,756; 8,717,664; 8,786,935;        8,797,634; 8,810,899; 8,830,559; 8,873,129; 8,902,153;        8,902,491; 8,917,439; 8,964,282; 9,013,783; 9,116,412;        9,146,439; 9,164,207; 9,170,467; 9,170,468; 9,182,646;        9,195,111; 9,199,441; 9,268,191; 9,285,649; 9,293,511;        9,341,916; 9,360,733; 9,361,836; 9,383,623; and 9,423,666; and        U.S. Patent Applications Publication Nos. 2008/0043318;        2008/0048970; 2009/0225398; 2010/0156780; 2011/0043543;        2012/0326957; 2013/0242378; 2013/0278995; 2014/0055840;        2014/0078576; 2014/0340430; 2014/0340736; 2014/0362213;        2015/0103394; 2015/0118390; 2015/0124345; 2015/0198858;        2015/0234250; 2015/0268531; 2015/0301246; 2016/0011484;        2016/0026062; 2016/0048054; 2016/0116816; 2016/0116818; and        2016/0140909;    -   (h) Methods for driving displays; see for example U.S. Pat. Nos.        5,930,026; 6,445,489; 6,504,524; 6,512,354; 6,531,997;        6,753,999; 6,825,970; 6,900,851; 6,995,550; 7,012,600;        7,023,420; 7,034,783; 7,061,166; 7,061,662; 7,116,466;        7,119,772; 7,177,066; 7,193,625; 7,202,847; 7,242,514;        7,259,744; 7,304,787; 7,312,794; 7,327,511; 7,408,699;        7,453,445; 7,492,339; 7,528,822; 7,545,358; 7,583,251;        7,602,374; 7,612,760; 7,679,599; 7,679,813; 7,683,606;        7,688,297; 7,729,039; 7,733,311; 7,733,335; 7,787,169;        7,859,742; 7,952,557; 7,956,841; 7,982,479; 7,999,787;        8,077,141; 8,125,501; 8,139,050; 8,174,490; 8,243,013;        8,274,472; 8,289,250; 8,300,006; 8,305,341; 8,314,784;        8,373,649; 8,384,658; 8,456,414; 8,462,102; 8,514,168;        8,537,105; 8,558,783; 8,558,785; 8,558,786; 8,558,855;        8,576,164; 8,576,259; 8,593,396; 8,605,032; 8,643,595;        8,665,206; 8,681,191; 8,730,153; 8,810,525; 8,928,562;        8,928,641; 8,976,444; 9,013,394; 9,019,197; 9,019,198;        9,019,318; 9,082,352; 9,171,508; 9,218,773; 9,224,338;        9,224,342; 9,224,344; 9,230,492; 9,251,736; 9,262,973;        9,269,311; 9,299,294; 9,373,289; 9,390,066; 9,390,661; and        9,412,314; and U.S. Patent Applications Publication Nos.        2003/0102858; 2004/0246562; 2005/0253777; 2007/0091418;        2007/0103427; 2007/0176912; 2008/0024429; 2008/0024482;        2008/0136774; 2008/0291129; 2008/0303780; 2009/0174651;        2009/0195568; 2009/0322721; 2010/0194733; 2010/0194789;        2010/0220121; 2010/0265561; 2010/0283804; 2011/0063314;        2011/0175875; 2011/0193840; 2011/0193841; 2011/0199671;        2011/0221740; 2012/0001957; 2012/0098740; 2013/0063333;        2013/0194250; 2013/0249782; 2013/0321278; 2014/0009817;        2014/0085355; 2014/0204012; 2014/0218277; 2014/0240210;        2014/0240373; 2014/0253425; 2014/0292830; 2014/0293398;        2014/0333685; 2014/0340734; 2015/0070744; 2015/0097877;        2015/0109283; 2015/0213749; 2015/0213765; 2015/0221257;        2015/0262255; 2015/0262551; 2016/0071465; 2016/0078820;        2016/0093253; 2016/0140910; and 2016/0180777 (these patents and        applications may hereinafter be referred to as the MEDEOD        (MEthods for Driving Electro-optic Displays) applications);    -   (i) Applications of displays; see for example U.S. Pat. Nos.        7,312,784 and 8,009,348; and    -   (j) Non-electrophoretic displays, as described in U.S. Pat. No.        6,241,921; and U.S. Patent Applications Publication Nos.        2015/0277160; and U.S. Patent Application Publications Nos.        2015/0005720 and 2016/0012710.

Many of the aforementioned patents and applications recognize that thewalls surrounding the discrete microcapsules in an encapsulatedelectrophoretic medium could be replaced by a continuous phase, thusproducing a so-called polymer-dispersed electrophoretic display, inwhich the electrophoretic medium comprises a plurality of discretedroplets of an electrophoretic fluid and a continuous phase of apolymeric material, and that the discrete droplets of electrophoreticfluid within such a polymer-dispersed electrophoretic display may beregarded as capsules or microcapsules even though no discrete capsulemembrane is associated with each individual droplet; see for example,U.S. Pat. No. 6,866,760. Accordingly, for purposes of the presentapplication, such polymer-dispersed electrophoretic media are regardedas sub-species of encapsulated electrophoretic media.

A related type of electrophoretic display is a so-called microcellelectrophoretic display. In a microcell electrophoretic display, thecharged particles and the fluid are not encapsulated withinmicrocapsules but instead are retained within a plurality of cavitiesformed within a carrier medium, typically a polymeric film. See, forexample, U.S. Pat. Nos. 6,672,921 and 6,788,449.

Although electrophoretic media are often opaque (since, for example, inmany electrophoretic media, the particles substantially blocktransmission of visible light through the display) and operate in areflective mode, many electrophoretic displays can be made to operate ina so-called shutter mode in which one display state is substantiallyopaque and one is light-transmissive. See, for example, U.S. Pat. Nos.5,872,552; 6,130,774; 6,144,361; 6,172,798; 6,271,823; 6,225,971; and6,184,856. Dielectrophoretic displays, which are similar toelectrophoretic displays but rely upon variations in electric fieldstrength, can operate in a similar mode; see U.S. Pat. No. 4,418,346.Other types of electro-optic displays may also be capable of operatingin shutter mode. Electro-optic media operating in shutter mode can beused in multi-layer structures for full color displays; in suchstructures, at least one layer adjacent the viewing surface of thedisplay operates in shutter mode to expose or conceal a second layermore distant from the viewing surface.

An encapsulated electrophoretic display typically does not suffer fromthe clustering and settling failure mode of traditional electrophoreticdevices and provides further advantages, such as the ability to print orcoat the display on a wide variety of flexible and rigid substrates.(Use of the word printing is intended to include all forms of printingand coating, including, but without limitation: pre-metered coatingssuch as patch die coating, slot or extrusion coating, slide or cascadecoating, curtain coating; roll coating such as knife over roll coating,forward and reverse roll coating; gravure coating; dip coating; spraycoating; meniscus coating; spin coating; brush coating; air knifecoating; silk screen printing processes; electrostatic printingprocesses; thermal printing processes; ink jet printing processes;electrophoretic deposition (See U.S. Pat. No. 7,339,715); and othersimilar techniques.) Thus, the resulting display can be flexible.Further, because the display medium can be printed (using a variety ofmethods), the display itself can be made inexpensively.

As indicated above most simple prior art electrophoretic mediaessentially display only two colors. Such electrophoretic media eitheruse a single type of electrophoretic particle having a first color in acolored fluid having a second, different color (in which case, the firstcolor is displayed when the particles lie adjacent the viewing surfaceof the display and the second color is displayed when the particles arespaced from the viewing surface), or first and second types ofelectrophoretic particles having differing first and second colors in anuncolored fluid (in which case, the first color is displayed when thefirst type of particles lie adjacent the viewing surface of the displayand the second color is displayed when the second type of particles lieadjacent the viewing surface). Typically the two colors are black andwhite. If a full color display is desired, a color filter array may bedeposited over the viewing surface of the monochrome (black and white)display. Displays with color filter arrays rely on area sharing andcolor blending to create color stimuli. The available display area isshared between three or four primary colors such as red/green/blue (RGB)or red/green/blue/white (RGBW), and the filters can be arranged inone-dimensional (stripe) or two-dimensional (2×2) repeat patterns. Otherchoices of primary colors or more than three primaries are also known inthe art. The three (in the case of RGB displays) or four (in the case ofRGBW displays) sub-pixels are chosen small enough so that at theintended viewing distance they visually blend together to a single pixelwith a uniform color stimulus (‘color blending’). The inherentdisadvantage of area sharing is that the colorants are always present,and colors can only be modulated by switching the corresponding pixelsof the underlying monochrome display to white or black (switching thecorresponding primary colors on or off). For example, in an ideal RGBWdisplay, each of the red, green, blue and white primaries occupy onefourth of the display area (one sub-pixel out of four), with the whitesub-pixel being as bright as the underlying monochrome display white,and each of the colored sub-pixels being no lighter than one third ofthe monochrome display white. The brightness of the white color shown bythe display as a whole cannot be more than one half of the brightness ofthe white sub-pixel (white areas of the display are produced bydisplaying the one white sub-pixel out of each four, plus each coloredsub-pixel in its colored form being equivalent to one third of a whitesub-pixel, so the three colored sub-pixels combined contribute no morethan the one white sub-pixel). The brightness and saturation of colorsis lowered by area-sharing with color pixels switched to black. Areasharing is especially problematic when mixing yellow because it islighter than any other color of equal brightness, and saturated yellowis almost as bright as white. Switching the blue pixels (one fourth ofthe display area) to black makes the yellow too dark.

U.S. Pat. Nos. 8,576,476 and 8,797,634 describe multicolorelectrophoretic displays having a single back plane comprisingindependently addressable pixel electrodes and a common,light-transmissive front electrode. Between the back plane and the frontelectrode is disposed a plurality of electrophoretic layers. Displaysdescribed in these applications are capable of rendering any of theprimary colors (red, green, blue, cyan, magenta, yellow, white andblack) at any pixel location. However, there are disadvantages to theuse of multiple electrophoretic layers located between a single set ofaddressing electrodes. The electric field experienced by the particlesin a particular layer is lower than would be the case for a singleelectrophoretic layer addressed with the same voltage. In addition,optical losses in an electrophoretic layer closest to the viewingsurface (for example, caused by light scattering or unwanted absorption)may affect the appearance of images formed in underlying electrophoreticlayers.

Attempts have been made to provide full-color electrophoretic displaysusing a single electrophoretic layer. For example, U.S. Pat. No.8,917,439 describes a color display comprising an electrophoretic fluidthat comprises one or two types of pigment particles dispersed in aclear and colorless or colored solvent, the electrophoretic fluid beingdisposed between a common electrode and a plurality of pixel or drivingelectrodes. The driving electrodes are arranged to expose a backgroundlayer. U.S. Pat. No. 9,116,412 describes a method for driving a displaycell filled with an electrophoretic fluid comprising two types ofcharged particles carrying opposite charge polarities and of twocontrast colors. The two types of pigment particles are dispersed in acolored solvent or in a solvent with non-charged or slightly chargedcolored particles dispersed therein. The method comprises driving thedisplay cell to display the color of the solvent or the color of thenon-charged or slightly charged colored particles by applying a drivingvoltage that is about 1 to about 20% of the full driving voltage. U.S.Pat. Nos. 8,717,664 and 8,964,282 describe an electrophoretic fluid, anda method for driving an electrophoretic display. The fluid comprisesfirst, second and third type of pigment particles, all of which aredispersed in a solvent or solvent mixture. The first and second types ofpigment particles carry opposite charge polarities, and the third typeof pigment particles has a charge level being less than about 50% of thecharge level of the first or second type. The three types of pigmentparticles have different levels of threshold voltage, or differentlevels of mobility, or both. None of these patent applications disclosefull color display in the sense in which that term is used below.

SUMMARY

Disclosed herein are improved methods of driving full colorelectrophoretic displays and method for identifying waveforms for fullcolor electrophoretic displays using these drive methods. In one aspect,a method of driving an electrophoretic display is disclosed.

The driving method includes providing an electrophoretic mediumcomprising four sets of particles, wherein each particle set has adifferent optical characteristic and a different charge characteristic,disposing the electrophoretic medium between a first light transmittingelectrode and a second electrode, providing a voltage driver configuredto provide at least five voltage levels, a high negative voltage, amedium negative voltage, a zero voltage, a medium positive voltage, anda high positive voltage, and driving the electrophoretic medium to adesired optical state by providing a push-pull waveform. Such apush-pull waveform includes a first positive portion composed of a firstpulse and a second pulse, the first pulse having a first positivemagnitude and a first time width and the second pulse having a secondpositive magnitude and a second time width. The push-pull waveformadditionally includes a second negative portion composed of a thirdpulse and a fourth pulse, the third pulse having a first negativemagnitude and a third time width and the fourth pulse having a secondnegative magnitude and a fourth time width. The first positivemagnitude, the second positive magnitude, the first negative magnitude,and the second negative magnitude are all non-zero, and at least threeof the first, second, third, and fourth time widths are non-zero. In anembodiment, the first set of particles is reflective and second, third,and fourth sets of particles are subtractive. In an embodiment, two ofthe sets of particles are positively charged and two of the sets ofparticles are negatively charged. In an embodiment, one of the sets ofparticles are positively charged and three of the sets of particles arenegatively charged. In an embodiment, three of the sets of particles arepositively charged and one of the sets of particles are negativelycharged. In an embodiment, the second electrode comprises a plurality ofpixel electrodes arranged in an array. In an embodiment, the secondelectrode is light transmitting. In an embodiment, the high negativevoltage is between −30V and −20V, the medium negative voltage is between−20V and −2V, the medium positive voltage is between 2V and 20V, and thehigh positive voltage is between 20V and 30V.

In another aspect, a method of identifying an enhanced push-pullwaveform. The method of identifying an enhanced push-pull waveformincludes selecting a finite set of voltages for driving anelectrophoretic display, wherein the set includes at least fivedifferent voltage levels, selecting a finite time width of time forcandidate waveforms, calculating all waveforms having a first positiveportion composed of a first pulse and a second pulse, wherein the firstpulse has a first positive magnitude and a first time width and thesecond pulse has a second positive magnitude and a second time width,and also having a second negative portion composed of a third pulse anda fourth pulse, the third pulse having a first negative magnitude and athird time width and the fourth pulse having a second negative magnitudeand a fourth time width. The first positive magnitude, the secondpositive magnitude, the first negative magnitude, and the secondnegative magnitude each have a value from the finite set of voltages,and the sum of the first pulse width, the second pulse width, the thirdpulse width, and the fourth pulse width equals the finite time width.The final step is calculating an optical state produced by each of thecandidate waveforms using a model of an electrophoretic display havingan electrophoretic medium comprising four sets of particles, whereineach particle set has a different optical characteristic and a differentcharge characteristic, and the electrophoretic medium is disposedbetween a first light transmitting electrode and a second electrode, andselecting a waveform to produce a targeted optical state. In anembodiment, selecting comprises comparing a target color to a predictedoutput color. In an embodiment, the selected waveforms are input into aphysical electrophoretic display including an electrophoretic mediumcomprising four sets of particles, wherein each particle set has adifferent optical characteristic and a different charge characteristic,and the electrophoretic medium is disposed between a first lighttransmitting electrode and a second electrode. In an embodiment, thecolor output of the physical electrophoretic display is evaluated andcompared to the target color. In an embodiment, the finite set ofvoltages includes a high negative voltage between −30V and −20V, amedium negative voltage between −20V and −2V, a medium positive voltagebetween 2V and 20V, and a high positive voltage between 20V and 30V. Inan embodiment, the finite set of voltages includes −27V, 0V, and +27V.In an embodiment, the first set of particles is reflective and second,third, and fourth sets of particles are subtractive. In an embodiment,two of the sets of particles are positively charged and two of the setsof particles are negatively charged. In an embodiment, one of the setsof particles are positively charged and three of the sets of particlesare negatively charged. In an embodiment, three of the sets of particlesare positively charged and one of the sets of particles are negativelycharged.

BRIEF DESCRIPTION OF DRAWINGS

The patent or application file contains at least one drawing executed incolor. Copies of this patent or patent application publication withcolor drawing(s) will be provided by the Office upon request and paymentof the necessary fee.

FIG. 1 is a schematic cross-section showing the positions of the variouscolored particles in an electrophoretic medium of the present inventionwhen displaying black, white, the three subtractive primary and thethree additive primary colors.

FIG. 2A shows in schematic form four types of different pigmentparticles used in a multi-particle electrophoretic medium.

FIG. 2B shows in schematic form four types of different pigmentparticles used in a multi-particle electrophoretic medium.

FIG. 2C shows in schematic form four types of different pigmentparticles used in a multi-particle electrophoretic medium.

FIG. 3 illustrates an exemplary equivalent circuit of a single pixel ofan electrophoretic display.

FIG. 4 shows the layers of an exemplary electrophoretic color display.

FIG. 5 shows the simple push pull waveforms that can be used to achievea set of primary colors in an optimized system including one reflective(white) particle, and three subtractive (cyan, yellow, magenta)particles.

FIG. 6 illustrates the set of voltage pulses available to be used with aseven level driver of an electrophoretic display. Every waveform that isavailable to drive an electrophoretic medium is some combination ofthese voltage pulses.

FIG. 7 illustrates an algorithm for identifying enhanced push pullwaveforms.

FIG. 8 shows an exemplary enhanced push pull waveform.

FIG. 9 shows an exemplary enhanced push pull waveform.

FIG. 10 shows 10,000 final color states achieved by enhanced push pullwaveforms using a model of a metal oxide TFT backplane and a fourparticle ACeP-type electrophoretic medium.

FIG. 11 shows a subset of DC-balanced EPP waveforms using a model of ametal oxide TFT backplane and a four particle ACeP-type electrophoreticmedium.

FIG. 12A and FIG. 12B compare calculated DC-imbalanced (FIG. 12A) andDC-balanced (FIG. 12B) waveforms to achieve a specific green color.

FIG. 13A and FIG. 13B compare calculated DC-imbalanced (FIG. 13A) andDC-balanced (FIG. 13B) waveforms to achieve a specific green color.

DETAILED DESCRIPTION

The invention details methods for identifying enhanced push pullwaveforms for driving a multi-particle color electrophoretic medium, forexample, wherein at least two of the particles are colored andsubtractive and at least one of the particles is scattering. Typically,such a system includes a white particle and cyan, yellow, and magentasubtractive primary colored particles. Such a system is shownschematically in FIG. 1 , and it can provide white, yellow, red,magenta, blue, cyan, green, and black at every pixel.

In the instance of ACeP, each of the eight principal colors (red, green,blue, cyan magenta, yellow, black and white) corresponds to a differentarrangement of the four pigments, such that the viewer only sees thosecolored pigments that are on the viewing side of the white pigment(i.e., the only pigment that scatters light). It has been found thatwaveforms to sort the four pigments into appropriate configurations tomake these colors need at least five voltage levels (high positive, lowpositive, zero, low negative, high negative). See FIG. 1 . To achievethe wider range of colors, additional voltage levels must be used forfiner control of the pigments, e.g., seven voltage levels, e.g., ninevoltage levels. The invention provides methods for identifying enhancedpush pull waveforms to drive such an electrophoretic medium so that theyrefreshes of pixel colors are faster, less flashy, and result in a colorspectrum that is more pleasing to the viewer.

The three particles providing the three subtractive primary colors,e.g., for an ACeP system, may be substantially non-light-scattering(“SNLS”). The use of SNLS particles allows mixing of colors and providesfor more color outcomes than can be achieved with the same number ofscattering particles. These thresholds must be sufficiently separatedrelative to the voltage driving levels for avoidance of cross-talkbetween particles, and this separation necessitates the use of highaddressing voltages for some colors. In addition, addressing the coloredparticle with the highest threshold also moves all the other coloredparticles, and these other particles must subsequently be switched totheir desired positions at lower voltages. Such a step-wisecolor-addressing scheme produces flashing of unwanted colors and a longtransition time.

As already mentioned, FIG. 1 of the accompanying drawings is a schematiccross-section showing the positions of the various particles in anACeP-type electrophoretic medium when displaying black, white, the threesubtractive primary colors and the three additive primary colors. InFIG. 1 , it is assumed that the viewing surface of the display is at thetop (as illustrated), i.e., a user views the display from thisdirection, and light is incident from this direction. As already noted,in preferred embodiments only one of the four particles used in theelectrophoretic medium of the present invention substantially scatterslight, and in FIG. 1 this particle is assumed to be the white pigment.This light-scattering white particle forms a white reflector againstwhich any particles above the white particles (as illustrated in FIG. 1) are viewed. Light entering the viewing surface of the display passesthrough these particles, is reflected from the white particles, passesback through these particles and emerges from the display. Thus, theparticles above the white particles may absorb various colors and thecolor appearing to the user is that resulting from the combination ofparticles above the white particles. Any particles disposed below(behind from the user's point of view) the white particles are masked bythe white particles and do not affect the color displayed. Because thesecond, third and fourth particles are substantiallynon-light-scattering, their order or arrangement relative to each otheris unimportant, but for reasons already stated, their order orarrangement with respect to the white (light-scattering) particles iscritical.

More specifically, when the cyan, magenta and yellow particles lie belowthe white particles (Situation [A] in FIG. 1 ), there are no particlesabove the white particles and the pixel simply displays a white color.When a single particle is above the white particles, the color of thatsingle particle is displayed, yellow, magenta and cyan in Situations[B], [D] and [F] respectively in FIG. 1 . When two particles lie abovethe white particles, the color displayed is a combination of those ofthese two particles; in FIG. 1 , in Situation [C], magenta and yellowparticles display a red color, in Situation [E], cyan and magentaparticles display a blue color, and in Situation [G], yellow and cyanparticles display a green color. Finally, when all three coloredparticles lie above the white particles (Situation [H] in FIG. 1 ), allthe incoming light is absorbed by the three subtractive primary coloredparticles and the pixel displays a black color.

It is possible that one subtractive primary color could be rendered by aparticle that scatters light, so that the display would comprise twotypes of light-scattering particle, one of which would be white andanother colored. In this case, however, the position of thelight-scattering colored particle with respect to the other coloredparticles overlying the white particle would be important. For example,in rendering the color black (when all three colored particles lie overthe white particles) the scattering colored particle cannot lie over thenon-scattering colored particles (otherwise they will be partially orcompletely hidden behind the scattering particle and the color renderedwill be that of the scattering colored particle, not black).

It would not be easy to render the color black if more than one type ofcolored particle scattered light.

FIG. 1 shows an idealized situation in which the colors areuncontaminated (i.e., the light-scattering white particles completelymask any particles lying behind the white particles). In practice, themasking by the white particles may be imperfect so that there may besome small absorption of light by a particle that ideally would becompletely masked. Such contamination typically reduces both thelightness and the chroma of the color being rendered. In theelectrophoretic medium of the present invention, such colorcontamination should be minimized to the point that the colors formedare commensurate with an industry standard for color rendition. Aparticularly favored standard is SNAP (the standard for newspaperadvertising production), which specifies L*, a* and b* values for eachof the eight primary colors referred to above. (Hereinafter, “primarycolors” will be used to refer to the eight colors, black, white, thethree subtractive primaries and the three additive primaries as shown inFIG. 1 .)

FIGS. 2A and 2B show schematic cross-sectional representations of thefour pigment types (1-4; 5-8) used in an ACeP-type electrophoreticdisplay. In FIG. 2A, the polymer shell adsorbed to the core pigment isindicated by the dark shading, while the core pigment itself is shown asunshaded. A wide variety of forms may be used for the core pigment:spherical, acicular or otherwise anisometric, aggregates of smallerparticles (i.e., “grape clusters”), composite particles comprising smallpigment particles or dyes dispersed in a binder, and so on as is wellknown in the art. The polymer shell may be a covalently-bonded polymermade by grafting processes or chemisorption as is well known in the art,or may be physisorbed onto the particle surface. For example, thepolymer may be a block copolymer comprising insoluble and solublesegments.

In the embodiment of FIG. 2A, first and second particle types preferablyhave a more substantial polymer shell than third and fourth particletypes. The light-scattering white particle is of the first or secondtype (either negatively or positively charged). In the discussion thatfollows it is assumed that the white particle bears a negative charge(i.e., is of Type 1), but it will be clear to those skilled in the artthat the general principles described will apply to a set of particlesin which the white particles are positively charged.

Additionally, as depicted in FIG. 2B, it is not required that the firstand second particle types have differential polymer shells as comparedto the third and fourth particle types. As shown in FIG. 2B, sufficientdifferential charge on the four particles will allow for electrophoreticcontrol of the particles and creation of the desired color at theviewing surface. For example, particle 5 may have a negative charge ofgreater magnitude than particle 7, while particle 6 has a greatermagnitude positive charge as compared to particle 8. It is also possiblethat other combinations of polymer functionality and charge (or particlesize) can be used; however, it must be the case that all four particlescan be separated from each other in the presence of suitable electricfields, e.g., lower voltage electric fields that can be produced withcommercial digital electronics.

In a system of FIG. 2A, the present invention the electric fieldrequired to separate an aggregate formed from mixtures of particles oftypes 3 and 4 in the suspending solvent containing a charge controlagent is greater than that required to separate aggregates formed fromany other combination of two types of particle. The electric fieldrequired to separate aggregates formed between the first and secondtypes of particle is, on the other hand, less than that required toseparate aggregates formed between the first and fourth particles or thesecond and third particles (and of course less than that required toseparate the third and fourth particles).

In FIG. 2A the core pigments comprising the particles are shown ashaving approximately the same size, and the zeta potential of eachparticle, although not shown, is assumed to be approximately the same.What varies is the thickness of the polymer shell surrounding each corepigment. As shown in FIG. 2A, this polymer shell is thicker forparticles of types 1 and 2 than for particles of types 3 and 4.

It is not necessary in the present invention that all the coloredpigments behave as described above with reference to FIGS. 2A and 2B. Asshown in FIG. 2C, the third particle may have a substantial polymershell and may have a wide range of charge, including weakly positive. Inthis case the surface chemistry of the third particle must be differentfrom that of the first particle. For example, the first particle my beara covalently-attached silane shell to which is grafted a polymer thatmay be comprised of acrylic or styrenic monomers that are preferablyhydrophobic. The third particle may comprise a polymer shell that is notcovalently attached, but is deposited onto the surface of the coreparticle by dispersion polymerization. In such cases the invention isnot limited to the mechanism described above with reference to FIGS. 2Aand 2B.

To obtain a high-resolution display, individual pixels of a display mustbe addressable without interference from adjacent pixels. One way toachieve this objective is to provide an array of non-linear elements,such as transistors or diodes, with at least one non-linear elementassociated with each pixel, to produce an “active matrix” display. Anaddressing or pixel electrode, which addresses one pixel, is connectedto an appropriate voltage source through the associated non-linearelement. Typically, when the non-linear element is a transistor, thepixel electrode is connected to the drain of the transistor, and thisarrangement will be assumed in the following description, although it isessentially arbitrary and the pixel electrode could be connected to thesource of the transistor. Conventionally, in high resolution arrays, thepixels are arranged in a two-dimensional array of rows and columns, suchthat any specific pixel is uniquely defined by the intersection of onespecified row and one specified column. The sources of all thetransistors in each column are connected to a single column electrode,while the gates of all the transistors in each row are connected to asingle row electrode; again the assignment of sources to rows and gatesto columns is conventional but essentially arbitrary, and could bereversed if desired. The row electrodes are connected to a row driver,which essentially ensures that at any given moment only one row isselected, i.e., that there is applied to the selected row electrode aselect voltage such as to ensure that all the transistors in theselected row are conductive, while there is applied to all other rows anon-select voltage such as to ensure that all the transistors in thesenon-selected rows remain non-conductive. The column electrodes areconnected to column drivers, which place upon the various columnelectrodes voltages selected to drive the pixels in the selected row totheir desired optical states. (The aforementioned voltages are relativeto a common front electrode which is conventionally provided on theopposed side of the electro-optic medium from the non-linear array andextends across the whole display.) After a pre-selected interval knownas the “line address time” the selected row is deselected, the next rowis selected, and the voltages on the column drivers are changed so thatthe next line of the display is written. This process is repeated sothat the entire display is written in a row-by-row manner The timebetween addressing in the display is known as a “frame.” Thus, a displaythat is updated at 60 Hz has frames that are 16 msec.

Conventionally, each pixel electrode has associated therewith acapacitor electrode such that the pixel electrode and the capacitorelectrode form a capacitor; see, for example, International PatentApplication WO 01/07961. In some embodiments, N-type semiconductor(e.g., amorphous silicon) may be used to from the transistors and the“select” and “non-select” voltages applied to the gate electrodes can bepositive and negative, respectively.

FIG. 3 of the accompanying drawings depicts an exemplary equivalentcircuit of a single pixel of an electrophoretic display. As illustrated,the circuit includes a capacitor 10 formed between a pixel electrode anda capacitor electrode. The electrophoretic medium 20 is represented as acapacitor and a resistor in parallel. In some instances, direct orindirect coupling capacitance 30 between the gate electrode of thetransistor associated with the pixel and the pixel electrode (usuallyreferred to a as a “parasitic capacitance”) may create unwanted noise tothe display. Usually, the parasitic capacitance 30 is much smaller thanthat of the storage capacitor 10, and when the pixel rows of a displayis being selected or deselected, the parasitic capacitance 30 may resultin a small negative offset voltage to the pixel electrode, also known asa “kickback voltage”, which is usually less than 2 volts. In someembodiments, to compensate for the unwanted “kickback voltage”, a commonpotential V_(com), may be supplied to the top plane electrode and thecapacitor electrode associated with each pixel, such that, when V_(com)is set to a value equal to the kickback voltage (V_(KB)), every voltagesupplied to the display may be offset by the same amount, and no netDC-imbalance experienced.

A set of waveforms for driving a color electrophoretic display havingfour particles is described in U.S. Pat. No. 9,921,451, incorporated byreference herein. In U.S. Pat. No. 9,921,451, seven different voltagesare applied to the pixel electrodes: three positive, three negative, andzero. However, in some embodiments, the maximum voltages used in thesewaveforms are higher than that can be handled by amorphous siliconthin-film transistors. In such instances, suitable high voltages can beobtained by the use of top plane switching. It is costly andinconvenient, however, to use as many separate power supplies as thereare V. settings when top plane switching is used. Furthermore, top planeswitching is known to increase kickback, thereby degrading the stabilityof the color states.

Methods for fabricating an ACeP-type electrophoretic display have beendiscussed in the prior art. The electrophoretic fluid may beencapsulated in microcapsules or incorporated into microcell structuresthat are thereafter sealed with a polymeric layer. The microcapsule ormicrocell layers may be coated or embossed onto a plastic substrate orfilm bearing a transparent coating of an electrically conductivematerial. This assembly may be laminated to a backplane bearing pixelelectrodes using an electrically conductive adhesive. Alternatively, theelectrophoretic fluid may be dispensed directly on a thin open-cell gridthat has been arranged on a backplane including an active matrix ofpixel electrodes. The filled grid can then be top-sealed with anintegrated protective sheet/light-transmissive electrode.

FIG. 4 shows a schematic, cross-sectional drawing (not to scale) of adisplay structure 200 of an ACeP-type electrophoretic display. Indisplay 200 the electrophoretic fluid is illustrated as being confinedto microcups, although equivalent structures incorporating microcapsulesmay also be used. Substrate 202, which may be glass or plastic, bearspixel electrodes 204 that are either individually addressed segments orassociated with thin film transistors in an active matrix arrangement.(The combination of substrate 202 and electrodes 204 is conventionallyreferred to as the back plane of the display.) Layer 206 is an optionaldielectric layer according to the invention applied to the backplane.(Methods for depositing a suitable dielectric layer are described inU.S. patent application Ser. No. 16/862,750, incorporated by reference.)The front plane of the display comprises transparent substrate 222 thatbears a transparent, electrically conductive coating 220. Overlyingelectrode layer 220 is an optional dielectric layer 218. Layer (orlayers) 216 are polymeric layer(s) that may comprise a primer layer foradhesion of microcups to transparent electrode layer 220 and someresidual polymer comprising the bottom of the microcups. The walls ofthe microcups 212 are used to contain the electrophoretic fluid 214. Themicrocups are sealed with layer 210 and the whole front plane structureis adhered to the backplane using electrically-conductive adhesive layer208. Processes for forming the microcups are described in the prior ar,e.g., in U.S. Pat. No. 6,930,818. In some instance, the microcups areless than 20 μm in depth, e.g., less than 15 μm in depth, e.g., lessthan 12 μm in depth, e.g., about 10 μm in depth, e.g., about 8 μm indepth.

Most commercial electrophoretic displays use amorphous silicon basedthin-film transistors (TFTs) in the construction of active matrixbackplanes (202/024) because of the wider availability of fabricationfacilities and the costs of the various starting materials.Unfortunately, amorphous silicon thin-film transistors become unstablewhen supplied gate voltages that would allow switching of voltageshigher than about ±15V. Nonetheless, as described below, the performanceof ACeP is improved when the magnitudes of the high positive andnegative voltages are allowed to exceed ±15V. Accordingly, as describedin previous disclosures, improved performance is achieved byadditionally changing the bias of the top light-transmissive electrodewith respect to the bias on the backplane pixel electrodes, also knownas top-plane switching. Thus, if a voltage of +30V (relative to thebackplane) is needed, the top plane may be switched to −15V while theappropriate backplane pixel is switched to +15V. Methods for driving afour-particle electrophoretic system with top-plane switching aredescribed in greater detail in, for example, U.S. Pat. No. 9,921,451.

There are several disadvantages to the top-plane switching approach.Firstly, when (as is typical) the top plane is not pixelated, but is asingle electrode extending over the whole surface of the display, itselectrical potential affects every pixel in the display. If it is set tomatch one of the voltages of the largest magnitude available from thebackplane (for example, the largest positive voltage) when this voltageis asserted on the backplane there will be no net voltage across theink. When any other available voltage is supplied to a backplane, therewill always be a voltage of negative polarity supplied to any pixel inthe display. Thus, if a waveform requires a positive voltage this cannotbe supplied to any pixel until the top plane voltage is changed. Atypical waveform for use in a multicolor display of the third embodimentuses multiple pulses of both positive and negative polarity, and thelengths of these pulses are not of the same length in waveforms used formaking different colors. In addition, the phase of the waveform may bedifferent for different colors: in other words, a positive pulse mayprecede a negative pulse for some colors, whereas a negative pulse mayprecede a positive pulse for others. To accommodate such cases, “rests”(i.e., pauses) must be built into the waveforms. In practice, thisresults in waveforms being much longer (by as much as a factor of two)than they ideally need to be.

Secondly, in top plane switching there are limits to the voltage levelsthat may be chosen. If the voltages applied to the top plane are denotedV_(t+) and V_(t−), respectively, and those applied to the back planeV_(b+) and V_(b−), respectively, in order to achieve a zero o voltcondition across the electrophoretic fluid it must be true that|V_(t+)|=V_(b+)| and |V_(t−)|=|V_(b−)| . However, it is not necessaryfor the magnitudes of the positive and negative voltages to be the same.

In prior embodiments of the Advanced Color electronic Paper (ACeP), thewaveform (voltage against time curve) applied to the pixel electrode ofthe backplane of a display of the invention is described and plotted,while the front electrode is assumed to be grounded (i.e., at zeropotential). The electric field experienced by the electrophoretic mediumis of course determined by the difference in potential between thebackplane and the front electrode and the distance separating them. Thedisplay is typically viewed through its front electrode, so that it isthe particles adjacent the front electrode which control the colordisplayed by the pixel, and if it is sometimes easier to understand theoptical transitions involved if the potential of the front electroderelative to the backplane is considered; this can be done simply byinverting the waveforms discussed below.

FIG. 5 shows typical waveforms (in simplified form) used to drive afour-particle color electrophoretic display system described above. Suchwaveforms have a simple “push-pull” structure: i.e., they consist of adipole comprising two pulses of opposite polarity. The magnitudes andlengths of these pulses determine the color obtained. At a minimum,there should be five such voltage levels. FIG. 5 shows high and lowpositive and negative voltages, as well as zero volts. Typically, “low”(L) refers to a range of about five-15V, while “high” (H) refers to arange of about 15-30V. In general, the higher the magnitude of the“high” voltages, the better the color gamut achieved by the display. The“medium” (M) level is typically around 15V; however, the value for Mwill depend somewhat on the composition of the particles, as well as theenvironment of the electrophoretic medium. In some embodiments, the highnegative voltage is between −30V and −20V, the medium negative voltageis between −20V and −2V, the medium positive voltage is between 2V and20V, and the high positive voltage is between 20V and 30V. For example,the high negative voltage is −27V, the medium negative voltage is −15V,the medium positive voltage is 15V, and the high positive voltage is27V. If only three voltages are available (i.e., +V_(high), 0, and−V_(high)) it may be possible to achieve the same result as addressingat a lower voltage (say, V_(high)/n where n is a positive integer>1) byaddressing with pulses of voltage V_(high) but with a duty cycle of 1/n.

Enhanced push-pull (EPP) waveforms can be achieved with more drivinglevels. For example, a seven-level driver might provide seven differentvoltages to the data lines during the update of a selected pixel of thedisplay (e.g., V_(H), V_(H)′, V_(H)″, 0, V_(L)″, V_(L)′, V_(L),; e.g.,+V_(H), +V_(M), +V_(L), 0, −V_(L), −V_(M), −V_(H)). The spacing betweendrive levels can be the same, or different, depending upon theformulation of the electrophoretic medium. For example, +V_(H)=27V,+V_(M)=15V, +V_(L)=5V, 0, −V_(L)=−5V, −V_(M)=−15V, =−27V. For example,+V_(H)=30V, +V_(M)=20V, +V_(L)=10V, 0, −V_(L)=−10V, −V_(M)=−20V,−V_(H)=−30V. Regardless, when using a seven-level driver to drive anactive matrix backplane having a single controller, the controller canonly update a given pixel one frame at a time. Accordingly, any enhancedpush pull waveform is composed of some combination of pulses, eachlasting a frame period, i.e., as shown in FIG. 6 . The resultingwaveform, used to achieve a desired optical state in the medium, isconstructed from some combination of the pulses of FIG. 6 , assumingthat such a waveform may have no, or some number, n, of each of thepulses of FIG. 6 .

Implementing seven-level drivers with sufficient voltage amplitude isdifficult with standard amorphous silicon backplanes. It has been foundthat using control transistors from less-common materials, which have ahigher electron mobility, allow the transistors to switch larger controlvoltages, for example ±30V, as needed to implement seven-level driving.Newly-developed active matrix backplanes may include thin filmtransistors incorporating metal oxide materials, such as tungsten oxide,tin oxide, indium oxide, and zinc oxide. In these applications, achannel formation region is formed for each transistor using such metaloxide materials, allowing faster switching of higher voltages, e.g.,within the range of about −27V to +27V. Such transistors typicallyinclude a gate electrode, a gate-insulating film (typically SiO₂), ametal source electrode, a metal drain electrode, and a metal oxidesemiconductor film over the gate-insulating film, at least partiallyoverlapping the gate electrode, source electrode, and drain electrode.Such backplanes are available from manufacturers such as Sharp/Foxconn,LG, and BOE. One preferred metal oxide material for such applications isindium gallium zinc oxide (IGZO). IGZO-TFT has 20-50 times the electronmobility of amorphous silicon. By using IGZO TFTs in an active matrixbackplane, it is possible to provide voltages of greater than 30V via asuitable display driver.

Using, e.g., a seven-level driver, enhanced push pull (EPP) waveformsmay use a much larger space of waveform shapes and durations to achievethe desired optical performance. EPP waveforms are restricted to becomposed of a finite number of pulses, either positive or negative,where N^(P)is a tractable number, where N is the number of possiblevoltage levels and P is the number of pulses. See, FIG. 6 . For example,if N=7, P<5. For a set of voltage level choices, fixed waveform length,and number of pulses, all possible waveforms can be enumerated. For eachpulse, we can have each of the N voltage levels, leading to N^(P) uniquevoltage permutations (with replacement), where P is the number ofpulses. For the pulse lengths, we can choose these subject to theconstraint that the total length of the waveform, M, is fixed. If weconsider the scenario with P pulses, there are N*(N−1)^(P) uniquevoltage level choices for the P pulses, given that adjacent pulsescannot be of the same length (this would be P−1 pulses). We can thencalculate the number of pulse lengths with as

$\begin{pmatrix}{M - 1} \\{P - 1}\end{pmatrix},$

wnere this is read as M−1 choose P−1 (the binomial coefficient). Insummation:

${\#{of}{wave}{forms}} = {{N( {N - 1} )}^{P - 1}\begin{pmatrix}{M - 1} \\{P - 1}\end{pmatrix}}$

The formulation describes the number of waveforms given the multi-pulsestructure. This also consists of testing every one frame change in pulselengths. In general, the number of waveforms could be reducedsignificantly by testing every D frames, which requires substitution inthe equations above:

$M^{\prime} = {\frac{M}{D}.}$

To calculate all possible unique pulse-based structures where P≤numpulses, we formulate,

${{\#{of}{wave}{forms}} = {\sum_{p = 1}^{P}{{N( {N - 1} )}^{p - 1}\begin{pmatrix}{M - 1} \\{p - 1}\end{pmatrix}}}},$

which yields after simplification,

${{\#{of}{wave}{forms}} = {N^{M} - {{N( {N - 1} )}^{P}\begin{pmatrix}{M - 1} \\P\end{pmatrix}{\,_{2}F_{1}}( {1,\ {{{- M} + P + 1};{P + 1};{1 - N}}} )}}},$

where ₂F₁ is the hypergeometric function.

Of course, identifying the “best” waveform is not a simple task. GivenN=7, P=3, M=42, the total number of unique waveforms is 206,640. Each ofthese 206,640 waveforms would need to be tested for a given set ofenvironmental conditions (e.g., light source and temperature), andaugmented with a prefix waveform to provide appropriate clearing (e.g.,a shaking pulse) such that the initial state of the medium matched theexpected start state for the waveform.

A more efficient way to identify preferred EPP waveforms is to virtuallyexecute each proposed EPP waveform in a surrogate model representing thefinal display construction. A specific electrophoretic displayconstruction can be represented by a transfer function. In its simplestform:

0(t)=f(V(t), x(0))

Where O(t) is the optical state as a function of time and f is afunction of the voltage applied to the display as a function of time,given some initial state of the system at t=0 (x(0)). Additional inputscan be specified here, including but not limited to temperature,relative humidity, and incident light spectrum. The function f can beestimated using a variety of means, for example an ab initio model builtfrom component measurements, however the preferred embodiment, describedhere, is one in which f is represented by a differentiable deep learningnetwork based upon a recurrent neural network architecture, describedhenceforth as f, as the true f is being approximated by the deeplearning-based modeling.

Once f is established, each enhanced push-pull (EPP) waveform can beevaluated on the surrogate model for the final optical state color valueachieved, as well as intermediate states (optical trace info), andsubsequently calculable quantities such as ghosting performance, voltagesensitivity, transition appearance (e.g., “flashiness”) and temperaturesensitivity. Any or all of these metrics can be combined into a totalcost function that identifies preferred EPP waveforms, which aresubsequently verified on the actual electrophoretic display under test.These subsequent measurements on the actual electrophoretic display canbe fed back into the deep learning model to provide further refinementsof f. This complete process is described in block format in FIG. 7 . Itshould be recognized that the method described in FIG. 7 is exhaustivewithin its parameterization, i.e., all possible permutations aresearched. Thus, the method naturally overcomes a common challenge of aparameterization, i.e., how to assure that the optimization algorithmsufficiently samples parameter space. The combination of active matrixdriving with a set clock cycle and a driver with finite voltage levelsgreatly reduces the parameter space, yet the output waveforms aremeaningful and immediately applicable in the physical display. Thus, theEPP tuning method can be mathematically exhaustive, requiring noadditional optimization when tuning the final waveform for a productiondisplay.

As shown in FIG. 7 , the process begins with selecting the waveformlength (710). As discussed above, limitations such as frame width,customer applications, and power consumption may constrain thiscalculation. Nonetheless, the method can be used for a variety ofwaveform lengths from 10 s of milliseconds to many seconds. In steps(720) and (730) the number of pulses is selected and the total voltageand number of voltage levels are selected, respectively, which again maybe limited by the cost and availability of storage media for thewaveforms and commercial production limitations such as the cost ofmultiple power supplies versus the extra expense of a variable powersupply. Once all of these factors are accumulated, a base set of uniquewaveforms is generated in step (740), whereupon each of the waveforms isevaluated against a color target in step (750). The color target may be,for example, an RGB color code or hex code for a digital image.Alternatively, the color target may be a Pantone color or CMYK printstandard. The waveform that achieves the closest outcome to the colortarget is output as the candidate waveform in step (760). This waveformmay be actually fed to a real four particle electrophoretic displaycorresponding to the modeled display, whereby the outcome is measuredwith a calibrated optical bench and compared to the target. In someembodiments, these measurements are fed back into the model via step(770). More details of a suitable calibrated optical bench forevaluating the output of a four particle electrophoretic display can befound at “Optical measurement standards for reflective e-paper topredict colors displayed in ambient illumination environments,” ColorResearch and Application, vol. 43, issue 6, pages 907-921 (2018), whichis incorporated by reference in its entirety.

Using the methods described above, subsets of color waveforms for anACeP-type system that are faster and less flashy are quickly isolatedfor further testing. Such push-pull waveforms may include dipoles thatare actually bifurcated (or trifurcated) into some combination of pulseheight and width of the relative polarity. For example, as shown in FIG.8 and FIG. 9 , an enhanced push pull waveform may include a firstportion of the negative dipole having a magnitude of V_(L) and a firstwidth t₁, as well as a second portion of the negative dipole having amagnitude of V_(L)′ and a second width t₂. The positive portion of thedipole can be a single pulse, e.g., of magnitude VH and third width t3,or the positive portion of the dipole can be bi- or tri-furcated asdictated by the model f and the user needs for the update (e.g., speed,energy consumption, color specificity). Of course, the mirror enhancedpush pull function, as illustrated in FIG. 9 , may be a better waveformfor the needs of the user.

Of course, achieving the desired color with push pull driving pulses iscontingent on the particles starting the process from a known state,which is unlikely to be the last color displayed on the pixel.Accordingly, a series of reset pulses precede the driving pulses, whichincreases the amount of time required to update a pixel from a firstcolor to a second color. The reset pulses are described in greaterdetail in U.S. Pat. No. 10,593,272, incorporated by reference. Thelengths of these pulses (refresh and address) and of any rests (i.e.,periods of zero voltage between them may be chosen so that the entirewaveform (i.e., the integral of voltage with respect to time over thewhole waveform) is DC balanced (i.e., the integral of voltage over timeis substantially zero). DC balance can be achieved by adjusting thelengths of the pulses and rests in the reset phase so that the netimpulse supplied in the reset phase is equal in magnitude and oppositein sign to the net impulse supplied in the address phase, during whichphase the display is switched to a particular desired color.

The use of the EPP waveform is superior to completely unconstrainedwaveforms in that the transition appearance is bounded to be a set of amaximum of P abrupt color changes. While unconstrained waveforms couldbe designed to reduce the number of color changes, or to have pleasingtransition appearance, it is a technically difficult problem requiringgreater parsing of training data and more computing power. This is mucheasier with EPP waveforms selected as described herein. Moreover, thisEPP tuning method allows for exhaustive enumeration of the square-pulsebased waveforms that have historically provided a good trade-off betweena simple waveform structure with managed transition appearance andcomplexity of optimization. It is also likely that preventing singleframe drives and the number of large transients makes the resulting EPPwaveforms more robust in other ways (temperature sensitivity, voltagesensitivity, robustness across manufacturing variability).

EXAMPLE

The methods described above were used to construct a model functiondescribing a metal oxide AM-TFT backplane and a four particleelectrophoretic medium including one reflective (white) particle andthree subtractive particles (cyan, magenta, and yellow). For a 42-framewaveform at 85 Hz (0.5s) each 3-pulse EPP waveform was tested (a totalof 206, 640 unique waveforms). Eight color targets were chosencorresponding to the colors of black, white, magenta, blue, cyan, green,yellow and red. The 10,000 waveforms with the closest final color stateto each of these eight targets were chosen to be evaluated further.These 10,000 final color states points are plotted on an a*-b* plot inFIG. 10 :

Interestingly, the methods herein provide greater insight when searchingfor other distinguishing features, such as ghosting or DC-balance. Asshown in FIG. 11 , it is possible to achieve many of the same colorstates using DC-balanced (triangles) or DC-imbalanced (circles)waveforms. Note the overlap between the DC-imbalanced EPP waveform(circle) and the DC-balanced EPP waveforms (triangle) at therepresentative color states in FIG. 11 . However, looking at the actualwaveforms, it is remarkable to see that, in some instances theDC-balanced and DC-imbalanced waveforms are quite similar in shape.Compare, for example FIGS. 12A and 12B, corresponding to the square inFIG. 11 and FIGS. 13A and 13B, corresponding to the star in FIG. 11 . Inthe instance of FIGS. 12A and 12B, there is very little differencebetween the DC-balanced and DC-imbalanced waveforms, whereas in FIGS.13A and 13B, the difference between the DC-balanced and DC-imbalancedwaveforms is quite pronounced.

It is notable in FIGS. 10 and 11 , that the preferred target colors(“X”s in FIG. 11 ) may not be achievable in a given ACeP-typeelectrophoretic display build, using EPP waveforms. This phenomenon isreproduced in physical displays.

Having thus described several aspects and embodiments of the technologyof this application, it is to be appreciated that various alterations,modifications, and improvements will readily occur to those of ordinaryskill in the art. Such alterations, modifications, and improvements areintended to be within the spirit and scope of the technology describedin the application. For example, those of ordinary skill in the art willreadily envision a variety of other means and/or structures forperforming the function and/or obtaining the results and/or one or moreof the advantages described herein, and each of such variations and/ormodifications is deemed to be within the scope of the embodimentsdescribed herein. Those skilled in the art will recognize, or be able toascertain using no more than routine experimentation, many equivalentsto the specific embodiments described herein. It is, therefore, to beunderstood that the foregoing embodiments are presented by way ofexample only and that, within the scope of the appended claims andequivalents thereto, inventive embodiments may be practiced otherwisethan as specifically described. In addition, any combination of two ormore features, systems, articles, materials, kits, and/or methodsdescribed herein, if such features, systems, articles, materials, kits,and/or methods are not mutually inconsistent, is included within thescope of the present disclosure.

1. A method of determining push-pull waveforms for driving anelectrophoretic display, comprising: determining a set of candidatewaveforms for driving the electrophoretic display; estimating an opticalstate produced by each of the candidate waveforms using a modelrepresenting the electrophoretic display, wherein the model includes atransfer function represented byO(t)=f(V(t), x(0)) where t is time, O(t) is the optical state of theelectrophoretic display as a function of t, V(t) is the voltage appliedto the electrophoretic display as a function of t, x(0) is an initialoptical state of the electrophoretic display at t =0, and f is afunction of V(t) and x(0); and identifying a push-pull waveform toproduce a targeted optical state based on the estimated optical statesproduced by the candidate waveforms.
 2. The method of claim 1, furthercomprising driving the electrophoretic display to produce a color outputusing the push-pull waveform identified to produce the targeted opticalstate.
 3. The method of claim 2, further comprising evaluating the coloroutput of the electrophoretic display and comparing the color output tothe target color.
 4. The method of claim 2, further comprising using thecolor output and associated waveform as training data for the model. 5.The method of claim 1, wherein determining the set of candidatewaveforms comprises: selecting a finite set of at least five differentvoltage levels for waveforms for driving the electrophoretic display;selecting a finite time width for the waveforms; and identifying a setof waveforms each having a positive portion and a negative portion,wherein each of the positive and negative portions comprises at leastone pulse, and at least one of the positive and negative portionscomprises two pulses having different voltage magnitudes eachcorresponding to one of the at least five different voltage levels,wherein a sum of pulse widths of the positive and negative portionsequals the finite time width.
 6. The method of claim 5, whereinselecting the finite time width includes comparing a target color to apredicted output color.
 7. The method of claim 5, wherein the finite setof at least five different voltage levels includes a high negativevoltage between −30V and −20V, a medium negative voltage between −20Vand −2V, a medium positive voltage between 2V and 20V, and a highpositive voltage between 20V and 30V.
 8. The method of claim 5, whereinthe finite set of at least five different voltage levels includes −27V,0V, and +27V.
 9. The method of claim 5, wherein the finite set of atleast five different voltage levels includes seven voltage levels: ahigh negative voltage, a medium negative voltage, a low negativevoltage, a zero voltage, a low positive voltage, a medium positivevoltage, and a high positive voltage.
 10. The method of claim 1, whereindetermining the set of candidate waveforms comprises: selecting a finiteset of voltages for driving the electrophoretic display, wherein the setof voltages includes at least five different voltage levels; selecting afinite time width of time for candidate waveforms; and calculating allwaveforms having a first positive portion composed of a first pulse anda second pulse, the first pulse having a first positive magnitude and afirst time width and the second pulse having a second positive magnitudeand a second time width, and a second negative portion composed of athird pulse and a fourth pulse, the third pulse having a first negativemagnitude and a third time width and the fourth pulse having a secondnegative magnitude and a fourth time width, wherein the first positivemagnitude, the second positive magnitude, the first negative magnitude,and the second negative magnitude each have a value from the finite setof voltages, and wherein the sum of the first pulse width, the secondpulse width, the third pulse width, and the fourth pulse width equalsthe finite time width.
 11. The method of claim 1, wherein theelectrophoretic display comprises an electrophoretic medium disposedbetween a first light transmitting electrode and a second electrode, theelectrophoretic medium including four sets of particles, wherein eachparticle set has a different optical characteristic and a differentcharge characteristic from other particle sets in the electrophoreticmedium.
 12. The method of claim 11, wherein the four sets of particlescomprises first, second, third, and fourth sets of particles, whereinsaid first set of particles is reflective and second, third, and fourthsets of particles are subtractive.
 13. The method of claim 12, whereintwo of the four sets of particles are positively charged and two of thefour sets of particles are negatively charged.
 14. The method of claim12, wherein one of the four sets of particles is positively charged andthree of the four sets of particles are negatively charged.
 15. Themethod of claim 12, wherein three of the four sets of particles arepositively charged and one of the four sets of particles are negativelycharged.
 16. The method of claim 1, wherein the model is adifferentiable deep learning model based on a recurrent neural networkarchitecture.